Fractional quantum ferroelectric control of spin-valley locking and valley Hall effects in altermagnetic monolayer Cr2S2

Fractional quantum multiferroics, arising from the coupling between fractional quantum ferroelectricity (FQFE) and altermagnetism (AM), provide a promising platform for nonvolatile control of momentum dependent spin splitting in systems with zero net magnetization. However, extending this FQFE-AM coupling to valley degrees of freedom and Berry curvature driven valley Hall effects remains largely unexplored. Here, using first-principles calculations, we demonstrate that monolayer Cr2S2 realizes a two dimensional FQFE-AM platform with two switchable FQFE states connected by composite symmetry operations combining a fractional lattice translation with time reversal or parity-time reversal. We show that FQFE switching reverses the AM spin-polarized band structure and interchanges the spin characters of the X and Y valleys without rotating the N\'eel vector, thereby enabling polarization switchable spin-valley locking. Moreover, the two FQFE states exhibit reversed Berry curvature distributions, which, together with the switched spin-valley locking, enable polarization controlled valley Hall effects under both electron and hole doping. These results demonstrate a symmetry based mechanism for nonvolatile electrical control of AM spin splitting, spin-valley locking, and valley Hall effects, offering a general route toward low-power valleytronic devices based on FQFE-AM coupling.